The Mexico international has been granted leave from their Olympic side this summer so he can look for a new club and prepare for the forthcoming season
Vela has spent several seasons on loan from the Emirates Stadium and will now pursue a permanent move as he looks for regular first-team football.
The 23-year-old told Hector Gonzalez, the director of Mexico's national teams, not to include him for selection in the London Games as he will be searching for a new club over the summer.
Gonzalez said to reporters: "He told us that he does not want to play for Arsenal and he will go to a different club.
"He asked [not to be called up] so he can play the pre-season and meet his new manager at his new club, because it is almost sure he will not continue on at Real Sociedad."
The director also added that the decision is on a 'personal' basis as well as a 'professional' one and that not to expect to see the Mexican international until pre-season.
"Carlos Vela asked on a personal and professional level that he not be selected for any of the Mexican national teams."